image quantization using hsi based on bacteria foraging

85Research Cell: An International Journal of Engineering Sciences ISSN: 2229-6913 Issue July 2012, Vol. 6

© 2012 Journal Anu Books Authors are responsible for any plagiarism issues.

Image Quantization using HSI based on BacteriaForaging Optimization

1Dharminder Kumar, 2Vinay Chopra1Student, M.Tech., 2Assistant Professor,

Department of Computer Science & Engg,D.A.V. I.E.T., Jalandhar, Punjab

Abstract: Bacteria Foraging Optimization a nature-inspired optimization has drawnthe attention of researchers because of its efficiency in solving real-world optimizationproblems arising in several application domains. Color image quantization is animportant process of representing true color images using a small number of colors.Existing color reduction techniques tend to alter image color structure and distribution.Thus the researchers are always finding alternative strategies for color quantization.In cylindrical color spaces like HSI, color is represented by hue, saturation andintensity. These components are closer to the way human perceives and describescolor. Hue, saturation and intensity can also reveal image features that are not soobvious in other color spaces. The objective of this research work, is to design analgorithm for Image Quantization using HSI color space based on Bacteria ForagingOptimization. To implement and test the proposed algorithm. To compare the designedalgorithm with other quantization techniques. The conducted experiments indicatethat proposed algorithm generally results in a significant improvement of image qualitycompared to other well-known approaches.

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Dharminder Kumar, Vinay Chopra

Keywords: Color reduction, Bacteria Foraging Optimization, HSI color space,Euclidean distance, Swarm intelligence.

1. Introduction

Bacterial foraging behaviours are used as a source of engineeringapplications and computational model. A few models have been developedto bacterial foraging behaviours and been applied for solving practicalproblems [1, 9, 18]. Among them, Bacterial Foraging Optimization (BFO) isa population-based numerical optimization algorithm. Until date, BFO hasbeen applied successfully to some engineering problems, such as optimalcontrol [12], harmonic estimation [14], transmission loss reduction [16] andmachine learning [13].

1.1 Bacterial Foraging Optimization

AlgorithmDuring foraging of the real bacteria, locomotion is achieved by a set of

tensile flagella. Flagella help an E.coli bacterium to tumble or swim, whichare two basic operations performed by a bacterium at the time of foraging.When they rotate the flagella in the clockwise direction, each flagellum pullson the cell. That results in the moving of flagella independently and finallythe bacterium tumbles with lesser number of tumbling whereas in a harmfulplace it tumbles frequently to find a nutrient gradient. Moving the flagella inthe counterclockwise direction helps the bacterium to swim at a very fastrate. In the above-mentioned algorithm the bacteria undergoes chemotaxis,where they like to move towards a nutrient gradient and avoid noxiousenvironment. Generally the bacteria move for a longer distance in a friendlyenvironment. When they get food in sufficient, they are increased in lengthand in presence of suitable temperature they break in the middle to from anexact replica of itself. This phenomenon inspired Passino to introduce anevent of reproduction in Bacteria Foraging Optimization algorithm. Due tothe occurrence of sudden environmental changes or attack, the chemotactic



progress may be destroyed and a group of bacteria may move to someother places or some other may be introduced in the swarm of concern.This constitutes the event of elimination-dispersal in the real bacterialpopulation, where all the bacteria in a region are killed or a group is dispersedinto a new part of the environment.

The original Bacterial Foraging Optimization system consists of threeprincipal mechanisms, namely, chemo taxis, reproduction, and elimination-dispersal. These are described as follows [18].

1.1.1 Chemotaxis:

In the original BFO, a unit walk of the bacteria with random directionrepresents a “tumble” and a unit walk with the same direction in the laststep indicates a “run”. Suppose represents the bacterium at jth

chemotactic, kth reproductive, and lth elimination-dispersal step. C(i) is thechemotactic step size during each run or tumble (i.e., runlength unit). Thenin each computational chemotactic step, the movement of the ith bacteriumcan be represented as

...(1.1)

Where (i) is the direction vector of the jth chemotactic step. When thebacterial movement is run, (i) is the same with the last chemotactic step;otherwise, (i) is a random vector whose elements lie in [–1, 1].With themovement of run or tumble taken at each step of the chemotaxis process,a step fitness, denoted as J(i, j, k, l), will be evaluated[18].

1.1.2 Reproduction

The fitness value of each bacterium is calculated as the sum of the stepfitness during its life, that is

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Where Nc is the maximum step in a chemotaxis process. All bacteriaare sorted in descending order according to health status. In the reproductionstep, only the first half of population survives. The surviving population isdivided into two identical ones, which are then placed in the same locationsat which their parents were. Thus the total population of bacteria keepsconstant [18].

1.1.3 Elimination and Dispersal

The chemotaxis provides a basis for searching the local best solution,and the reproduction process speeds up the convergence which has beensimulated by the classical BFO. The bacteria with the best positions arekept and the remaining bacteria population is killed. The bacteria with bestpositions are then moved to another position within the environment [18].

1.1.4 BFO Algorithm

In what follows we briefly outline the original BFO algorithm step by step.

Step 1. Initialize parameters n, S, Nc, Ns, Nre , Ned , Ped,C(i) (i = 1, 2, . . . , S), i, where

n : dimension of the search space,S : the number of bacteria in the colony,Nc : Chemotactic steps,Ns :: Swim steps,Nre: : Reproductive steps,Ned : Elimination and dispersal steps,Ped : Probability of elimination,Step 2. Elimination-dispersal loop: l = l + 1.



Step 3. Reproduction loop: k =k +1.Step 4. Chemotaxis loop: j = j + 1.Substep 4.1. For i= 1= 1, 2, . . ., S, take a chemotactic step for bacterium ias follows.

Substep 4.2. Compute fitness function, J(i, j, k, l).

Substep 4.3. Let last j = J(i, j, k, l) to save this value since we may find bettervalue via a run.

Substep 4.4. Tumble. Generate a random vector

with each element m(i), m =1, 2, . . . , n, a random number on [-1, 1].

Substep 4.5. Move. Let

...(1.2)

This results in a step of size C(i) in the direction of the tumble for bacterium i.

Substep 4.6. Compute J(i, j +1, k, l) with

Substep 4.7. Swimming.Let m = 0 (counter for swim length).While m < Ns (if has not climbed down too long), the following hold.

• Let m= m + 1.• If J(i, j + 1, k, l)< jlast let jlast = J(i, j+ 1, k, l), then another step of size C(i)in this same direction will be taken as (2.2) and use the new generated.

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• i (j +1, k, l) to compute the new J(i, j+ 1, k, l).

• Else let m = s N .

Substep 4.8. Go to next bacterium (i +1). If i S, go to Substep 4.2 toprocess the next bacterium.Step 5. If j < Nc , go to Step 3. In this case, continue chemotaxis since the lifeof the bacteria is not over.Step 6. Reproduction.Substep 6.1. For the given k and l, and for each i = 1, 2, . . . , S, let

....(1.3)

be the health of the bacteria. Sort bacteria in order of ascending values( Jhealth ).

Substep 6.2. The Sr bacteria with the highest Jhealth values die and the otherSr bacteria with the best values split and the copies that are made are placedat the same location as their parent.

Step 7. If k < Nre , go to Step 2. In this case the number of specifiedreproduction steps is not reached and start the next generation in thechemotactic loop.

Step 8. Elimination-dispersal:for i =1, 2, . . . , S, with probability Ped , eliminate and disperse each bacterium,which results in keeping the number of bacteria in the population constant.



To do this, if a bacterium is eliminated, simply disperse one to a randomlocation on the optimization domain. If l < Ned , then go to Step 2; otherwiseend [15].

1.2 Color image quantization

Color image quantization is an important process of representing true colorimages using a small number of colors. With a good color quantizationalgorithm and some lossy compression algorithms (such as ones used by.jpg formats), the same image quality (at least visually) can mostly berestored from a much smaller file. The color image quantization can reducenot only storage requirement but also the transfer time of the image. Thesereductions are quite important for multimedia applications in the Internetwhere the communication delays are very concerned. Moreover, the colorimage quantization can be implemented as a preprocessing step for imagecompression algorithm. The color image quantization algorithm typically consists of four phases. The first phase, called sampling the original image, computes the image

histogram for color statistics i.e. a number of distinct colors and theirfrequencies.

The second phase, called colormap design, chooses the best possibleset of representative colors from the color statistics.

The third phase, called pixel mapping, maps each color in the originalimage to a representative color in the colormap.

The fourth phase, called image quantizing, redraws the image byreplacing the original color in every pixel with a representative color.applied.

Color quantization is important because quantized image can be usedin many applications including the following.

It can be used in lossy compression techniques.

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It is suitable for mobile and hand-held devices where memory is usuallysmall [10].

It is suitable for low-cost color display and printing devices where only asmall number of colors can be displayed or printed simultaneously [7].

Most graphics hardware use color lookup tables with a limited numberof colors [6].

1.3 HSI color model

The choice of the color space can be a very important decision whichcan dramatically influence the results of the processing. The knowledge ofvarious color spaces can ease the choice of the appropriate colour space.Color is the way the HVS (the human visual system) measures a part of theelectromagnetic spectrum, approximately between 300 and 830 nm. A colorspace is a notation by which we can specify colours, ie the human perceptionof the visible electromagnetic spectrum.When humans view a color object, we tend to describe it by its hue,saturation, and brightness.

Hue is an attribute that describes a pure color.saturation gives a mesaure of the degree to which a pure color is diluted bywhite light.

Brightness is a subjective descriptor that is practically impossible tomeasure.

It embodies the achromatic description of intensity and is a key factor indescribing color sensation. We do know that intensity (gray level) is a mostuseful descriptor of monochromatic images. This quantity definitely ismeasurable and easily interpretable. The Hue component describes thecolor itself in the form of an angle between [0,360] degrees. 0 degree meanred, 120 means green 240 means blue. 60 degrees is yellow, 300 degreesis magenta. The Saturation component signals how much the color is polluted



with white color. The range of the S component is [0,1]. The Intensity rangeis between [0,1] and 0 means black, 1 means white.

While implementing the color image quantization using Bacteria ForagingOptimization we have considered the HSI color model as compared to RGBand LAB color model. RGB and LAB color space has some drawbackswhich make researchers look to the other color spaces in computer visiontasks. One drawback is high correlation between individual componentscaused by aliasing of spectral sensitivity curves of three types of cones.Further, the individual components does not correspond the way humanperceives and describes colors [1]. For example, it is hard to say, solelylooking at the color, how much of individual components comprise the color.In cylindrical color spaces like HSI color is represented by hue, saturationand intensity (value, brightness). These components are closer to the wayhuman perceives and describes color. Hue, saturation and intensity canalso reveal image features that are not so obvious in RGB and LAB colorspace. Also, in HSI color space chromatic (hue and saturation) andachromatic (intensity) information are separated.

1.4 Euclidean distance

A central problem in image recognition and computer vision is determiningthe distance between images. Considerable efforts have been made to defineimage distances that provide intuitively reasonable results.Among all the image metrics, Euclidean distance is the most commonlyused due to its simplicity. The key advantages of this metric are:1) Relative insensitivity to small perturbation (deformation);2) Simplicity of computation;3) It can be efficiently embedded in most of the powerful image recognition

techniques.Euclidean distance between two points in HSI color model is defined as

follows:

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..1.4

Where

HSI is the total color difference. A single HSI limit value may be set tobe used in evaluating color matches [8]. In this research work, the fitnessfunction is taken as Euclidean distance to find out the distance between twofood sources i.e. colors. Color difference calculated using Euclidean distancemethod are believed to correlate better with visual assessment than colordifferences calculated using other instrumental systems.

The rest of the paper is organized as follows. Section 2 surveys relatedwork in the field of color image quantization. The proposed algorithm ispresented in section 3, while an experimental evaluation of the algorithm isprovided in section 4. Finally, section 5 concludes the paper and providesguidelines for future research.

2. Related Work In The Field Of Color

Image QuantizationSeveral heuristic techniques for color image quantization have been

proposed in the literature. Some of them are discussed below.The popularity algorithm generates the colormap by finding the densest

regions in color distribution of the image. Hence, it simply selects the K



colors with the highest occurrences from the image histogram and usesthese K colors as the representative colors in the colormap[23].

The median-cut algorithm uses the splitting approach to repeatedly dividethe color space into two smaller individual cells containing an approximatelyequal number of pixels at each step. The orientation of cutting plane is normalto one of the coordinate axes with a largest range of image pixels and passthrough the median point of the color distribution projected on this axis. Atthe end of this operation, the final cells contain an equal number of imagepixels[11].

The variance-based algorithm is schematically similar to the mediancutalgorithm, with an exception that, at each step, a cell for further partition isthe cell with the largest weighted variances of color distribution. The cuttingplane is chosen to be perpendicular to the coordinate axis where the expectedvariance is most reduced[2].

The octree algorithm relies on a tree structure. The root of the octree isan entire cell and at each level of the tree each node has eight successors.The maximum depth of the octree is 8. At level 8, the terminal nodes of theoctree are individual colors. The octree is then reduced by a process thatreplaces the terminal node with their parent node containing an average ofthe color in the terminal node. This process continues until the number ofterminal nodes is equal K. Finally, the K terminal nodes are chosen as therepresentative colors in the colormap[11].

M. G. Omran [11] in his paper proposes Color image quantization basedon PSO. The proposed approach is of the class of quantization techniquesthat performs clustering of the color space. The proposed algorithm randomlyinitializes each particle in the swarm to contain K centroids (i.e. color triplets).The K-means clustering algorithm is then applied to each particle at a user-specified probability to refine the chosen centroids. Each pixel is thenassigned to the cluster with the closest centroid. The PSO is then applied torefine the centroids obtained from the Kmeans algorithm.

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[21] In this paper the bacteria foraging optimization is applied to LAB colormodel for image quantization. The CMC distance metric is used for colordifference between pixels. Color elimination and reproduction is done byevaluating the CMC distance. The threshold value of CMC distance is usedfor comparisons.

3. Proposed Algorithm

Bacteria Foraging Optimization is a population oriented algorithm usedto search optimal solution. In this research each Pixel of the image isconsidered as bacteria and the color of the pixel is considered as bacteriafood. The aim of the proposed algorithm is to minimize the food sources i.e.to reduce the number of colors in the image. In this research, all the pixelsinitially have some color and the purpose of this research is to optimize thenumber of colors in the image. All the colors in the image are evaluated asthe number of pixels having that color. This evaluation defines the healthstatus of all the colors present in the image. Depending upon the healthstatus of the colors, all the colors in the image are divided into two categoriespopular colors and unpopular colors. If the health status of the color is highi.e. the color is present on too many pixels then that color is considered aspopular color and all other colors whose health status is poor are consideredunpopular colors. All the pixels in the image are compared with every otherpixel in the image to find the most similar color to be eliminated. The fitnessfunction is taken as Euclidean distance to find out the distance between twofood sources i.e. colors. Based on the value of euclidean distance betweensimilar colors elimination of one of the colors is done. After this eliminationprocess the health status of all the colors is evaluated again because afterelimination the health status of colors may change. After the eliminationprocess, the unpopular colors are compared based on euclidean distancevalues to combine colors to produce a new color. This process of producing



the new color is called as reproduction. The colors from which the newcolor is produced are killed.

BFO Consist of following basic principal echanisms:- Chemo-taxis. Elimination. Reproduction. Dispersal.

3.1 Chemo-taxis

The motion patterns that the bacteria will generate in the presence ofchemical attractants and repellents are called chemo-taxis. For E. coli, thisprocess was simulated by two different moving ways: run or tumble. ABacterium alternates between these two modes of operation its entire lifetime.The bacterium sometimes tumbles after a tumble or tumbles after a run.This alternation between the two modes will move the bacterium, and thisenables it to “search” for nutrients. In this research, each bacteria takes aunit step of size one in the same direction to find its nutrient i.e. each pixeltakes a unit step of size one to find the most similar color. If the pixel find themost similar color after a unit walk fulfilling the fitness function i.e. Euclideandistance then it is called as swim where the pixel color is replaced with thecolor of that next pixel.

For two color of respective HSI image components (H11, S11, I11) and(H2, S2, I2), Euclidean distance metrics define two components for distancemeasure as follow:

Where

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HSI here represents the Euclidean distance between two colors. If themost similar color is not found at the immediate next pixel position then thebacterium i.e. the pixel run to the next pixel positions with the unit steps, tofind the most similar color. This process of swimming continued till themaximum number of similar colors is found.

3.2 Elimination

Elimination is performed in two steps. Primary elimination and secondaryelimination.Primary Elimination: In primary elimination if a pixel in the image foundsimilar color following the fitness function then one of them becomescandidate pixel for the elimination.Secondary Elimination: In secondary elimination firstly the health status isof all the colors in the image is evaluated. Then based on the health statusthe colors are divided into two categories surviving i.e. popular and the un-surviving i.e. unpopular colors. The un-surviving colors following the fitnessfunction become candidate for the elimination. In this research, aftercomparing the colors of all the pixels in the image the elimination of colorsin this step is based on the primary elimination.

3.3 Reproduction

All the colors in the image are evaluated as the number of pixels havingthat color.



Health status =

Where N represents the number of pixels having ith color. And Srepresents total number of pixels in the image. This evaluation defines thehealth status of all the colors present in the image. Depending upon thehealth status of the colors, all the colors in the image are divided into twocategories surviving colors and un-surviving colors. If the health status ofthe color is high then that pixel is considered as surviving color and all othercolors whose health status is poor are considered un-surviving colors. Theunpopular colors are compared and if the Euclidean distance between twounpopular colors is found less than threshold value then those two colorsare combined to produce a new color. This process of producing the newcolor is called as reproduction.

3.4 DispersalAs explained above in the reproduction, we can add new colors to our

color palette. The un-surviving colors from which the new color is producedare eliminated. Elimination in this step is performed according to thesecondary elimination. This new color is now dispersed i.e. allocated to theparents of new color.

In the classical BFO, the bacteria with the best positions are kept andthe remaining bacteria population is killed. The bacteria with best positionsare then moved to another position within the environment. In this research,the colors with poor health status are eliminated and the colors with highhealth status are kept. The new colors dispersed to other pixels in the imagewhere the parents of new color were present. In the classical BFO, only thefirst half of population survives.

In this research, instead of killing bacteria population the food sourcesare killed and reproduced. BFO has been implemented and validated on byapplying the algorithm on images as well phantom images.

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3.5 Proposed algorithmStep1. Initialize parameters

S , i , Ns , Nc , k , l , n , Nu , HSI (ki, ki+1)WhereS : Total number of pixels in the image (total number of bacteria).i : Total colors in the image (number of food sources).Ns : Number of swim steps (Ns =1).Nc : Number of chemo-tactic steps (Nc =1).ki : Color of the current pixel (Current bacteria).l : New color (new food source).ni : Number of pixels having same color (Number of bacteria following i thfood source).Nu : Number of pixels having unpopular color (Total number of bacteria withunpopular food source).

HSI ((ki1, ki+1)) : This is euclidean distance between Bacteria’s currentfood source and nearest food source).

Food sources are divided into categories popular and unpopulardepending upon how many bacteria are moving toward that particular foodsource. Colors in the image are divided into two categories surviving colorsand un-surviving colors depending upon how many pixels have the similarcolor.Step 2. Chemo-tactic step: Compute

...3.1

Where



Step 2. Elimination stepFor k = 1.........S. Take a chemo-tactic step of size one for pixel k as follows:

If HSI ((ki1, ki+1)) <= Dmax

Eliminate ki pixel’s color and all other pixels having ith color withki+1 pixel’s color.

Elsek = k +1END

END

Step 3. Reproduction and dispersal step

Health status =

Categorize the colors in the image into two categories popular and unpopulardepending upon the health status.Substep 3.1For k = 1.........Nu Take a chemo-tactic step of size one for pixel k as follows:

If ( ki = popular)Continue;

Else If HSI ((ki1, ki+1)) <= Dmax

l = ...3.2

Eliminate pixel’s color and pixel’s color. Disperse lth color at the pixelswere the parents of lth color were.END

END

Dmax is a constant to be chosen while evaluating similarity.

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4. Results And DiscussionsOur objective is to use the proposed Bacteria Foraging Optimization

algorithm for Color image quantization using HSI color model. BacteriaForaging Optimization using HSI color model has been validated by usingDmax = 0.205 and applying the algorithm on images as well as phantomimages by varying the size of image and number of bacteria. Phantomimages are also called as computer generated images. This categorycollects images that are scans, screen captures, photos, and/or illustrationsof the Phantom and related characters and intellectual properties. Thefollowing figures show input image with original number of colors and resultingimage with quantized colors.

Figure 4.1:Original image ‘Image1.bmp’ with 9719 colors on left

and Quantized image ‘Image1.bmp’with 5529 colors on right.



Figure 4.2:Original image ‘Parrots.jpg’ with 8806 colors on left

and Quantized image ‘Parrots.jpg’ with 5503 colors on right.

Figure 4.3:Original image ‘Phantom1.jpg’ with 4721 colors on left

and Quantized image “Phantom1.jpg’ with 2974 colors on right.

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Figure 4.4:Original image ‘Phantom2.jpg’

with 5918 colors on leftand Quantized image ‘Phantom2.jpg’ with 3754 colors on right.

Figure 4.5:Original image ‘Technology.png’ with 7643 colors on left

and Quantized image ‘Technology.png’ with 5042 colors on right.



Figure 4.6: Original image ‘Image2.png’ with 8824 colors on left side andQuantized image ‘Image2.png’ with 5740 colors right side.

The computational results which have been obtained using the proposedalgorithm are shown below in a table. These results have been analyzedbased on LMSE, Euclidean distance for images, Normalized Absolute Errorand Average Difference.

Table 4.1 Computational Result & Analysis of results based onLMSE, Euclidean distance, Average Difference and Normalized

Absolute Error

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From the above results it can be observed that perceptual uniformity isthere in the output image. There is no degradation in the image quality. Theprocessed image is visually similar to the input image. The performance ofproposed algorithm is evaluated based on LMSE, Euclidean distance forimages, Normalized Absolute Error and Average Difference. In this researchwork the results which have been achieved using Bacteria ForagingOptimization for color quantization using HSI color model are comparedwith the other approaches. The results of the proposed algorithm are analyzedby comparing it with the existing techniques of color image quantization.

The following figures shows the processed images based on BacteriaForaging Optimization for color quantization using HSI color model andprocessed images based on Bacteria Foraging Optimization for colorquantization using LAB color model.

Figure 4.13:Quantized image ‘Image2.png’ with 5756 colors using BFO-CIQ LAB on leftand Quantized image ‘Image2.png’ with 5740 colors using BFO-CIQ HSI on

right.



Figure 4.14:Quantized image ‘Phantom1.jpg’ with 3083 colors using CIQ LAB on left

and Quantized image ‘Phantom1.jpg’ with 2974 colors using BFO-CIQ HSIon right.

From the results shown above, the results obtained by using Bacteriaforaging optimization using HSI model are comparatively better than theprevious work.

5. Conclusions And Future Work

In this paper, we have presented Bacteria Foraging Optimizationalgorithm for color image quantization using HSI color model. Based on theresults presented in the previous chapter, I conclude that the imagequantization based on Bacteria foraging optimization using HSI color modelgives better results. The HSI color model eliminates the weakness of RGBcolor model and LAB model. In HSI color model hue, saturation and intensity(value, brightness) components are closer to the way human perceivesand describes color. Hue, saturation and intensity can also reveal imagefeatures that are not so obvious in RGB color space and LAB color space.In this research, Bacteria Foraging Optimization has been implemented onvarious types of images including the phantom images. This validates the

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proposed algorithm and it gives optimized results when implemented onthe phantom images.

5.1 Future Work

In the proposed algorithm we have to consider each pixel and for largeimages the proposed algorithm may become slow. So the further researchmay focus on some modification of the proposed algorithm to enhance thespeed. Further research work may focus on developing some new algorithmsrelated to bacterial foraging to decrease the computational cost and timeduring global optimization. Future research may try to apply the BacteriaForaging Optimization algorithm for color image quantization to other colorspaces.

6. Acknowledgements

I am extremely grateful to Assistant Professor Vinay Chopra,Department of CSE & I.T., DAVIET, Jalandhar helping in carrying thepresent work and acknowledged with reverential thanks. Without the wisecounsel and able guidance, would have been impossible to complete thiswork in this manner.

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image quantization using hsi based on bacteria foraging

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